What does "In each generation, 25% of offspring resulted from mutation without crossover" mean in the context of NEAT?
In genetic algorithms, mutation without crossover simply means that part of the population is randomly changed. In this case this is applied to 25% of the population.

The remaining 75% either remain unchanged (generally the best performing specimen), or will be combined with other specimen (using crossover). It's a bit more complex here, as the genome is connecting weights in networks, and they use 'species', where certain individuals are treated as separate groups from the rest of the population.